Traffic Engineering And Management 13. Vehicle Arrival Models : Count
Chapter 13
Vehicle Arrival Models : Count
13.1 Introduction
Modelling arrival of vehicle at section of road is an important step in traffic flow modelling.
It has important application in traffic flow simulation where vehicles are to be generated how
vehicles arrive at a section. Vehicle arrivals can be modelled in two inter-related ways; namely
modelling how many vehicle arrive in a given interval of time, or modelling what is the time
interval between the successive arrival of vehicles. The vehicle arrival is obviously a random
process. This is evident if one observe how vehicles are arriving at a cross section. Some time
several vehicles come together, but on other times, they come sparsely. The former approach the
random variables are always integer, ie., number of vehicle arrive in a given interval will always
be some integer. Here in this approach, a discrete distribution can be used to model the process.
Traditionally a Poisson distribution is used to model this process. In the later approach, the
random variables are positive real numbers, ie., the time interval between successive arrival of
vehicle can be any positive real value. Here, in this approach, a continuous distribution can be
used to model the vehicle arrival. Needless to say that both the approaches are looking at the
same phenomenon in two perspective and both the perspective must be inter-related. Suppose,
if we plot the arrival of vehicle at cross section as dot across a time axis, it may look like
Fig. 13:1. Let h1,h2, ... etc indicate the headways, then as mentioned earlier, they are some
real values. However the headways or inter arrival time can be modelled using some continuous
distribution. Also, let t1,t2,t3and t4are four equal time intervals, then the number of vehicles
arrived in each of these interval is an integer value. For example, in Fig. 13:1, 3, 2, 3 and 1
Time
t1t2t3t4
h1h2h3h4h5h6h7h8h9h10
Figure 13:1:
Dr. Tom V. Mathew, IIT Bombay 1 April 2, 2012
